**Time: ** Tuesday, Oct 25, 2016, 2:00pm @ MTH1311

**Speaker: ** Prof. Greg Coxson (United States Naval Acadamy)

**Title: ** Enumeration and Generation of Binary and Quad-Phase
Code PSL Equivalence Classes

**Abstract: ** The problem of optimizing binary and quad-phase
aperiodic autocorrelation sidelobe levels is notoriously difficult,
and likely NP-hard. Some have likened these problems to that of
seeking needles in a haystack. I have at times tried to find aspects
of these problems that can be used to predict behavior for all
code lengths N, but these efforts have always ended in frustration. However, recently, I posed a question about the binary case that
not only yielded an enumeration result for all code lengths N,
but even led to a similar result for the quad-phase case. A side
benefit of the work is a pair of simple algorithms for visiting, one-by-one, single representatives of each PSL equivalence class for any code length N of interest. Such algorithms can be employed, ideally in combination with other methods, to expedite searches for low-sidelobe binary and quad-phase codes. Interestingly, this process has also caused me to
learn some of the Basque language, and even some elements of the
Theories of Knots and Braids. I hope to find a way to work the associated
stories into my talk.
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